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   <div id="projectbrief">A light library for C# vector graphics</div>
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  <div class="headertitle"><div class="title">SmoothSpline.cs</div></div>
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<div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span><span class="comment">/*</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno">    2</span><span class="comment">    VectSharp - A light library for C# vector graphics.</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span><span class="comment">    Copyright (C) 2020-2022 Giorgio Bianchini</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span><span class="comment"></span> </div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno">    5</span><span class="comment">    This program is free software: you can redistribute it and/or modify</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span><span class="comment">    it under the terms of the GNU Lesser General Public License as published by</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span><span class="comment">    the Free Software Foundation, version 3.</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span><span class="comment"></span> </div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno">    9</span><span class="comment">    This program is distributed in the hope that it will be useful,</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno">   10</span><span class="comment">    but WITHOUT ANY WARRANTY; without even the implied warranty of</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span><span class="comment">    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span><span class="comment">    GNU Lesser General Public License for more details.</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span><span class="comment"></span> </div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span><span class="comment">    You should have received a copy of the GNU Lesser General Public License</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="comment">    along with this program. If not, see &lt;https://www.gnu.org/licenses/&gt;.</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span><span class="comment">*/</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span> </div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span><span class="keyword">using </span>System.Collections.Generic;</div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span><span class="keyword">using </span>System.Linq;</div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span> </div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespace_vect_sharp.html">VectSharp</a></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span>{</div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span>    <span class="comment">//derived from https://www.particleincell.com/wp-content/uploads/2012/06/bezier-spline.js</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span> </div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span>    <span class="keyword">internal</span> <span class="keyword">static</span> <span class="keyword">class </span>SmoothSpline</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span>    {</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span>        <span class="keyword">public</span> <span class="keyword">static</span> Point[] SmoothSplines(Point[] points)</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span>        {</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>            <span class="keywordtype">double</span>[] x = (from el in points select el.X).ToArray();</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>            <span class="keywordtype">double</span>[] y = (from el in points select el.Y).ToArray();</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span> </div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>            (<span class="keywordtype">double</span>[] p1, <span class="keywordtype">double</span>[] p2) px = ComputeControlPoints(x);</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>            (<span class="keywordtype">double</span>[] p1, <span class="keywordtype">double</span>[] p2) py = ComputeControlPoints(y);</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span> </div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>            List&lt;Point&gt; tbr = <span class="keyword">new</span> List&lt;Point&gt;();</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span> </div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; points.Length - 1; i++)</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>            {</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>                tbr.Add(<span class="keyword">new</span> Point(x[i], y[i]));</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>                tbr.Add(<span class="keyword">new</span> Point(px.p1[i], py.p1[i]));</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>                tbr.Add(<span class="keyword">new</span> Point(px.p2[i], py.p2[i]));</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>            }</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span> </div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>            tbr.Add(<span class="keyword">new</span> Point(x[x.Length - 1], y[x.Length - 1]));</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span> </div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>            <span class="keywordflow">return</span> tbr.ToArray();</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>        }</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span> </div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>        <span class="comment">/*computes control points given knots K, this is the brain of the operation*/</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>        <span class="keyword">private</span> <span class="keyword">static</span> (<span class="keywordtype">double</span>[] p1, <span class="keywordtype">double</span>[] p2) ComputeControlPoints(<span class="keywordtype">double</span>[] K)</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>        {</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>            <span class="keywordtype">int</span> n = K.Length - 1;</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span> </div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span> </div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>            <span class="keywordtype">double</span>[] p1 = <span class="keyword">new</span> <span class="keywordtype">double</span>[n];</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>            <span class="keywordtype">double</span>[] p2 = <span class="keyword">new</span> <span class="keywordtype">double</span>[n];</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span> </div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span> </div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>            <span class="comment">/*rhs vector*/</span></div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>            <span class="keywordtype">double</span>[] a = <span class="keyword">new</span> <span class="keywordtype">double</span>[n];</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>            <span class="keywordtype">double</span>[] b = <span class="keyword">new</span> <span class="keywordtype">double</span>[n];</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>            <span class="keywordtype">double</span>[] c = <span class="keyword">new</span> <span class="keywordtype">double</span>[n];</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>            <span class="keywordtype">double</span>[] r = <span class="keyword">new</span> <span class="keywordtype">double</span>[n];</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span> </div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>            <span class="comment">/*left most segment*/</span></div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>            a[0] = 0;</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>            b[0] = 2;</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>            c[0] = 1;</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>            r[0] = K[0] + 2 * K[1];</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span> </div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>            <span class="comment">/*internal segments*/</span></div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt; n - 1; i++)</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>            {</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>                a[i] = 1;</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>                b[i] = 4;</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>                c[i] = 1;</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>                r[i] = 4 * K[i] + 2 * K[i + 1];</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>            }</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span> </div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>            <span class="comment">/*right segment*/</span></div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>            a[n - 1] = 2;</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>            b[n - 1] = 7;</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>            c[n - 1] = 0;</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>            r[n - 1] = 8 * K[n - 1] + K[n];</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span> </div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>            <span class="comment">/*solves Ax=b with the Thomas algorithm (from Wikipedia)*/</span></div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt; n; i++)</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>            {</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>                <span class="keywordtype">double</span> m = a[i] / b[i - 1];</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>                b[i] = b[i] - m * c[i - 1];</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>                r[i] = r[i] - m * r[i - 1];</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>            }</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span> </div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>            p1[n - 1] = r[n - 1] / b[n - 1];</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = n - 2; i &gt;= 0; i--)</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>            {</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>                p1[i] = (r[i] - c[i] * p1[i + 1]) / b[i];</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>            }</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span> </div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>            <span class="comment">/*we have p1, now compute p2*/</span></div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n - 1; i++)</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>            {</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>                p2[i] = 2 * K[i + 1] - p1[i + 1];</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>            }</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span> </div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>            p2[n - 1] = 0.5 * (K[n] + p1[n - 1]);</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span> </div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>            <span class="keywordflow">return</span> (p1, p2);</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>        }</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span> </div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    }</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>}</div>
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